TRIPOLI (AFP) - Armed men attacked the home of Libya's new prime minister on Tuesday, two days after he won a parliamentary vote of confidence but with opposition to his proposed government rising.

Libya's General National Congress, or interim parliament, had elected 42-year-old businessman Ahmed Miitig as premier in a chaotic vote this month to replace Mr Abdallah al-Thani, who had resigned for security reasons.

"There was an attack with rockets and small arms on the prime minister's house" in Tripoli at 3:00 am (9:00 am, Singapore time), an aide to Mr Miitig said on condition of anonymity.

The premier and his family were in the house at the time, but escaped unharmed. His guards opened fire on the group, wounding two of them and arresting them, the official added.

The GNC passed a vote of confidence in Mr Miitig, who is backed by the Islamists, and his new cabinet amid rising lawlessness in the North African nation dogged by power struggles between rival former-rebel militias.

Libya has been awash with weapons since the NATO-backed uprising that toppled and killed longtime dictator Muammar Gaddafi in 2011.

Successive governments have struggled to control the myriad ex-rebel militias that have carved out fiefdoms across the country, and Mr Miitig is Libya's fifth premier since Mr Gaddafi's ouster.

He is due to lead a short transitional period until legislative elections are held on June 25, and the new parliament will replace the GNC and form a new cabinet.

Largely unknown to the public before his election, Mr Miitig assumed office with opposition to his mandate already mounting and with a renegade former general gathering support for an offensive in the eastern city of Benghazi.

Mr Khalifa Haftar launched a military drive on May 16 to crush Islamists in Benghazi, where near daily attacks blamed on jihadists had been targeted security forces, and since the beginning of his operation several other units have joined his forces.

The GNC has accused Mr Haftar of launching a coup but Mr Haftar said the Libyan people had given him a "mandate" to crush jihadist militants after thousands of people rallied in his support in Benghazi and Tripoli.

'ILLEGAL' ELECTION

Mr Miitig has tried to reach out to his critics, inviting them to take part in a "comprehensive national dialogue to complete state institutions".

In the speech published in Libyan press, Mr Miitig also committed to "pressing the battle against terrorists and those who threaten the security of the country," referring to jihadist groups in the restive east.

But just hours after Mr Miitig and his new cabinet were approved by the GNC, autonomist rebels who have been blockading eastern oil terminals said they did not recognise his government, labelling it "illegal".

"We reject the government of Ahmed Miitig," said Mr Ibrahim Jodhran, the self-proclaimed head of the Cyrenaica Political Bureau, a group demanding greater autonomy for Libya's eastern region.

Mr Jodhran also accused Islamist blocs in the GNC of "illegally imposing" Miitig's cabinet.

Former rebels who fought the Gaddafi regime have been blockading eastern oil ports since July last year, preventing crude exports and causing oil production to fall to 250,000 barrels per day, down from 1.5 billion bpd previously.

Adding to the confusion, the outgoing government published a letter on its website from the vice-president of the GNC, Ezzedine al-Awami, in which he urged it to continue its work, and called Miitig's election "illegal".

No official list of cabinet members has been published until now, and Libya's 2014 budget has yet to be passed because of deep political divisions within the GNC.

The situation in Libya has caused worry among its neighbours, and on Monday a spokesman for Tunisia's foreign ministry told AFP other North African countries would hold an "urgent meeting" on Libya.